Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 12}$ ${-2x+3y = 13}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $5y = 25$ $\dfrac{5y}{{5}} = \dfrac{25}{{5}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+2y = 12}\thinspace$ to find $x$ ${2x + 2}{(5)}{= 12}$ $2x+10 = 12$ $2x+10{-10} = 12{-10}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 5}$ into $\thinspace {-2x+3y = 13}\thinspace$ and get the same answer for $x$ : ${-2x + 3}{(5)}{= 13}$ ${x = 1}$